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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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Zenodo
2026
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| Acceso en línea: | https://doi.org/10.5281/zenodo.19413000 |
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- <p>Volume 44 certifies a finite <strong>three-branch Fourier-shell admissibility object</strong> for the <strong>KS→NS comparison family</strong> under the inherited <strong>Sigma_41 instrument lineage</strong>. The study object is the <strong>shell-membership law</strong> over the declared <strong>width-by-halfspan family</strong> emitted by the production notebook. Within the certified domain through <strong>halfspan 2.00</strong>, the admissibility object has <strong>three branches</strong>: a <strong>primary support-shell branch</strong>, a <strong>support-free substitute branch</strong>, and an <strong>exact higher-shell triad branch</strong>.</p> <p>The full declared family contains <strong>1,695 transition cells</strong> across <strong>66 declared (width, halfspan) pairs</strong>, and the certified three-branch law matches the measured admissibility oracle exactly, with <strong>zero mismatches</strong>, <strong>zero false positives</strong>, and <strong>zero false negatives</strong>. <strong>Branch 3</strong> admits an exact triad representative based on the shell set <strong>{sqrt(45), sqrt(49), sqrt(50)}</strong>, that is, <strong>{sqrt(45), 7, sqrt(50)}</strong>. The former residual sector left open by Volume 43 is absorbed exactly by this third branch, and <strong>no fourth branch is required</strong> on the certified domain through <strong>halfspan 2.00</strong>.</p> <p>The study uses the inherited locked <strong>KS→NS shell-law setting</strong> under the <strong>Sigma_41 lineage</strong>, a rebuilt production-state admissibility oracle <strong>A(c)</strong>, exact certification sweeps over the declared transition-cell family, and machine-readable artifact emission under the inherited RSI publication discipline. The certified object is a <strong>finite combinatorial shell-membership law</strong> on the declared scanning family, <strong>not</strong> a general transport theorem beyond that domain.</p> <p><strong>Certified Results:</strong></p> <ul> <li><strong>Exact three-branch shell law</strong> certified on the declared width-by-halfspan family through <strong>halfspan 2.00</strong></li> <li>Production certification sweep covers <strong>1,695 transition cells</strong></li> <li>Exact agreement between the declared law and the measured admissibility oracle</li> <li><strong>Zero mismatches</strong></li> <li><strong>Zero false positives</strong></li> <li><strong>Zero false negatives</strong></li> <li>Full certified partition: <strong>EXCLUDE = 901</strong>, <strong>Branch 1 = 712</strong>, <strong>Branch 2 = 6</strong>, <strong>Branch 3 = 76</strong></li> <li>The inherited two-branch law leaves a <strong>76-cell admissible residual</strong> on the certified domain</li> <li>Volume 44 certifies that <strong>all 76 residual cells are absorbed exactly by Branch 3</strong></li> <li><strong>No fourth branch is required</strong> on the certified domain through <strong>halfspan 2.00</strong></li> </ul> <p><strong>Certified Branch Structure:</strong></p> <ul> <li><strong>Branch 1</strong> — q_crit not in B, q_sup in B</li> <li><strong>Branch 2</strong> — q_crit not in B, q_sup not in B, q_branch_hi in B, q_branch_lo not in B</li> <li><strong>Branch 3</strong> — sqrt(45) in B, sqrt(49) in B, sqrt(50) in B, sqrt(20) not in B, sqrt(37) not in B, 6 not in B, and 5 not in B</li> </ul> <p><strong>Canonical Constructs:</strong></p> <p>Three-branch Fourier-shell admissibility law, <strong>Branch-3 triad representative</strong>, <strong>residual-sector closure certificate</strong>, exact admissibility-oracle agreement on the declared family, <strong>no-fourth-branch certificate</strong> through halfspan 2.00, <strong>Sigma_41 inherited instrument lineage</strong>.</p> <p><strong>Continuity:</strong></p> <p>Volume 44 continues the RSI shell-law program by converting the structured residual sector identified in Volume 43 from <strong>residual geometry</strong> into <strong>exact branch structure</strong>. The inherited two-branch law is preserved where it was already exact, and the formerly uncovered admissible sector is absorbed exactly by an additional branch clause in the same shell-membership language. The result is therefore a <strong>closed three-branch shell law</strong> on the certified declared family through <strong>halfspan 2.00</strong>.</p> <p><strong>Reproducibility:</strong></p> <p>Evidence for the certified claim set consists of the <strong>locked production notebook</strong>, the rebuilt production-state <strong>KS→NS admissibility oracle A(c)</strong>, the declared <strong>width-by-halfspan transition-cell sweep</strong>, exact certification totals emitted by the executable run, reader-facing export blocks, and the final artifact bundle under inherited <strong>RSI manifest discipline</strong>.</p> <p><strong>Scope Bound:</strong></p> <p>This volume does <strong>not</strong> certify <strong>uniqueness of the Branch-3 normal form</strong>, <strong>extension beyond halfspan 2.00</strong>, <strong>extension beyond the declared width range</strong>, or <strong>general transport beyond the declared KS→NS scanning family</strong>. It certifies only the <strong>bounded three-branch shell-law object</strong> stated above under the inherited <strong>Sigma_41 instrument lineage</strong>.</p>